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Modeling Star Distribution Using Spatial Poisson Process

Kostercová, Viktória LU (2025) In Bachelor’s Theses in Mathematical Sciences MASK11 20251
Mathematical Statistics
Abstract
This thesis explores the Poisson process in one and multiple dimensions, with particular focus
on its application to modeling the spatial distribution of stars. The theory of both homogeneous
and inhomogeneous Poisson processes is developed, along with key aspects such as thinning,
distribution of inter-arrival times and nearest neighbor distribution. These are then extended
to a three-dimensional setting.
Two main applications of the Poisson process are considered, both modeling stars as inde-
pendent points in three-dimensional space. First, we study the probability that two stars are
mutually nearest neighbors, with the help of the nearest neighbor distribution and spatial ge-
ometry. Second, we estimate the expected number of... (More)
This thesis explores the Poisson process in one and multiple dimensions, with particular focus
on its application to modeling the spatial distribution of stars. The theory of both homogeneous
and inhomogeneous Poisson processes is developed, along with key aspects such as thinning,
distribution of inter-arrival times and nearest neighbor distribution. These are then extended
to a three-dimensional setting.
Two main applications of the Poisson process are considered, both modeling stars as inde-
pendent points in three-dimensional space. First, we study the probability that two stars are
mutually nearest neighbors, with the help of the nearest neighbor distribution and spatial ge-
ometry. Second, we estimate the expected number of stars visible to the naked eye, in order to
derive the probability distribution function of this number. This involves applying thinning,
as stars that are not bright enough to be seen should be excluded. We consider processes with
both homogeneous and inhomogeneous intensity. (Less)
Popular Abstract
Have you ever wondered how many stars you can see in the night sky? Have you ever tried
to count them? Probably not - it would take ages. Unlike astronomical databases, statisti-
cians cannot give you the exact number, but they can o!er something else: the probability
distribution of the number of stars you might see.
Having that, we can answer many more questions. For example: How likely is it that you see a
certain number of stars? What is the expected number of visible stars? What is the expected
distance from the Sun to its nearest neighboring star? And how likely is it that the Sun is also
the nearest neighbor of that star?
To tackle these questions, we treat stars as randomly and independently located points in space
and... (More)
Have you ever wondered how many stars you can see in the night sky? Have you ever tried
to count them? Probably not - it would take ages. Unlike astronomical databases, statisti-
cians cannot give you the exact number, but they can o!er something else: the probability
distribution of the number of stars you might see.
Having that, we can answer many more questions. For example: How likely is it that you see a
certain number of stars? What is the expected number of visible stars? What is the expected
distance from the Sun to its nearest neighboring star? And how likely is it that the Sun is also
the nearest neighbor of that star?
To tackle these questions, we treat stars as randomly and independently located points in space
and apply a statistical model known as the Poisson process. This method is used for modeling
seemingly random sequences of events or points and despite its simplicity, provides a lot of
information about the events. Thorough theoretical treatment of the Poisson process and its
application to stars along with answering the aforementioned questions are the central topic
of this thesis. (Less)
Please use this url to cite or link to this publication:
author
Kostercová, Viktória LU
supervisor
organization
course
MASK11 20251
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor’s Theses in Mathematical Sciences
report number
LUNFMS-4080-2025
ISSN
1654-6229
other publication id
2025:K7
language
English
id
9199459
date added to LUP
2025-06-23 15:57:53
date last changed
2025-06-23 15:57:53
@misc{9199459,
  abstract     = {{This thesis explores the Poisson process in one and multiple dimensions, with particular focus
on its application to modeling the spatial distribution of stars. The theory of both homogeneous
and inhomogeneous Poisson processes is developed, along with key aspects such as thinning,
distribution of inter-arrival times and nearest neighbor distribution. These are then extended
to a three-dimensional setting.
Two main applications of the Poisson process are considered, both modeling stars as inde-
pendent points in three-dimensional space. First, we study the probability that two stars are
mutually nearest neighbors, with the help of the nearest neighbor distribution and spatial ge-
ometry. Second, we estimate the expected number of stars visible to the naked eye, in order to
derive the probability distribution function of this number. This involves applying thinning,
as stars that are not bright enough to be seen should be excluded. We consider processes with
both homogeneous and inhomogeneous intensity.}},
  author       = {{Kostercová, Viktória}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor’s Theses in Mathematical Sciences}},
  title        = {{Modeling Star Distribution Using Spatial Poisson Process}},
  year         = {{2025}},
}